Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
6 Issues per year
IMPACT FACTOR 2016: 0.783
5-year IMPACT FACTOR: 0.792
CiteScore 2016: 0.80
SCImago Journal Rank (SJR) 2016: 0.589
Source Normalized Impact per Paper (SNIP) 2016: 1.125
Mathematical Citation Quotient (MCQ) 2015: 0.43
Use of extrapolation in regularization methods
Extrapolation is a well-known tool for increasing the accuracy of approximation methods. We consider extrapolation of Tikhonov and Lavrentiev methods and iterated variants of these methods for solving linear ill-posed problems in Hilbert space. For extrapolated approximation we take the linear combination of n ≥ 2 approximations of the original method with different parameters and with proper coefficients, guaranteeing for extrapolated method higher qualification than in original method. Extrapolated approximation can be used for approximation to solution of the equation or for construction of a posteriori rules for choice of the regularization parameter in original method. As shown, extrapolating n Tikhonov or Lavrentiev approximations gives the same approximation as one gets in nonstationary implicit iterative method after n iterations with the same parameters. If the solution is smooth and δ is noise level of data, a proper choice of n = n(δ) guarantees for extrapolated Tikhonov approximation accuracy versus accuracy of Tikhonov approximation. Note that in a posteriori parameter choice in Tikhonov method often several approximations with different parameters are computed and then computation of their linear combination is an easy task.
Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.